Experiment 1: Error analysis and graph drawing
Assignments
Assignment 1
(7)
Assignment 2
(7)
Assignment 3
(7)
Assignment 4
(7)
Assignment 5
(7)
Total
(35)
Assignments:
1.
Apart from physics, curve fitting and data analysis is used in many areas. The table
given below shows the winning time at the 100 m race for men in the Olympic games.
Year
1896
1900
1904
1908
1912
1920
1924
1928
1932
1936
1948
1952
1956
1960
1964
Time
(secs)
12.0
11.0
11.0
10.8
10.8
10.8
10.6
10.8
10.3
10.3
10.3
10.4
10.5
10.2
10.0
(a)
Year
1968
1972
1976
1980
1984
1988
1992
1996
2000
2004
2008
2012
2016
2020
Time
(secs)
9.9
10.14
10.06
10.25
9.99
9.92
9.96
9.84
9.87
9.85
9.69
9.63
9.81
Plot the points on the given graph sheet..
(b) Determine the line of best fit and draw that line on the graph sheet. Based on your
analysis, predict the winning time for the 100 m race in the Olympics to be held
in 2020.
(c) Do you think the observed trend (decrease in the winning time) will continue
forever? Why?
2.
The angular positions () of the nth order maxima of a diffraction grating satisfy the
equation dsin = nHere d is the distance between the centres of successive slits of
the grating. Derive a relation connecting the error in  to the error in . Assuming that
d is known to be 1.6 m and n=1, calculate the error in determining the wavelength
 using the given equation  = 200. The least count of the spectrometer (used to
determine ) is 1’.
The error in determining  can be taken to be the least count of the spectrometer.
3.
The breaking strength of a certain kind of Polyester thread depends on its thickness as
shown in the data given below.
Thickness (mm):
0.8362
0.1194 0.1778 0.2032 0.2718 0.3150 0.3861 0.4724 0.5867
Strength (Kg-Wt):
0.7
1.4
3.2
5.0
6.6
9.5
14.1
20.0
0.7188
37.7
44.5
Guess the relation between the thickness and strength. Plot strength on the y axis and a
suitable power of thickness on the x axis. Determine the parameters of the best fit line.
4.The table given below shows the luminosity of some stars (relative to the luminosity of the
sun). The corresponding mass of the star (relative to the mass of the sun) is also given. Plot the
data given in the table on the log-log graph paper with L/Lsun on y axis and M/Msun on the x
axis. From the plot it should be clear that
L/Lsun = C (M/Msun)
a) Calculate and draw the straight line which best fits the given data and hence
determine the value of and C .
2)
3
4
4.5
6
8
9
10
10
50
100
400
1000
2500
5000
20000
M/Msun
L/Lsun
5. The resistance of a semiconducting sample over a certain temperature range is given as a
function of temperature (T) by the equation, R = Ro exp(Eg/2kT) where k is the
Boltzmann constant and Eg is the band gap of the semiconductor. (T is in Kelvin. And R
is in ohms).
T: 360
370
380
390
400
410
420
430
440
R: 1000
810
660
490
435
345
286
240
194
T: 450
460
470
480
490
500
R: 166
108
94
80
70
65
Plot the experimental data on suitable graph paper (semi-log) and find out the value of Ro and
Eg.